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НЕТРАДИЦ1ЙН1 ВИДИ ТРАНСПОРТУ. МАШИНИ ТА МЕХАН1ЗМИ
UDC 621.867.21
V. M. BOHOMAZ1*
1 Dep. «Military training of specialists of the State special service of transport», Dnepropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnepropetrovsk, Ukraine, 49010, tel. +38 (056) 793 19 09, e-mail [email protected], ORCID 0000-0001-5913-2671
RESEARCH OF DEPENDENCE OF BELT CONVEYER DRIVE POWER ON ITS DESIGN PARAMETERS
Purpose. A drive is one of the basic elements of belt conveyers. To determine the drive power it is necessary to conduct calculations by standard methodologies expounded in modern technical literature. Such calculations demand a fair amount of time. The basic design parameters of a belt conveyer include type of load, design efficiency, geometrical dimensions and path configuration, operation conditions. The article aims to build the parametric dependence of belt conveyer drive power on its design parameters, that takes into account standard dimensions and parameters of belts, idlers and pulleys. Methodology. The work examines a belt conveyer with two areas: sloping and horizontal. Using the methodology for pulling calculation by means of belt conveyer encirclement, there are built parametric dependences of pull forces in the characteristic conveyer path points on the type of load, design efficiency, geometrical dimensions and path configuration, operation conditions. Findings. For the belt conveyers of the considered type there are built parametric dependences of drive power on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions, taking into account the belt standard dimensions and corresponding assumptions in relation to idler and pulley types. Originality. This is the first developed parametric dependence of two-area (sloping and horizontal) belt conveyer drive power on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions that takes into account standard dimensions and parameters of belts, idlers and pulleys. Practical value. Use of the built drive power dependences on design parameters for the belt conveyers with sloping and horizontal areas gives an opportunity of relatively rapid determination of drive power approximate value at the design stage. Also it allows quality selection of its basic elements at specific design characteristics and requirements. The offered dependences can be used for determination of general character of drive power dependence on the project efficiency.
Keywords: conveyer; belt; drive; power; efficiency; load
Introduction
Transporting machines are important elements of transport and industrial construction sector. Continuous-transport machines are the foundation of the comprehensive mechanization of cargo handling, industrial processes, they increase productivity and efficiency. The most common type of continuous transport is belt conveyors. Belt conveyors are the continuous-type machines, the main ele-
ment of which is vertically closed rubber belt that encircles the end pulleys, one of which is usually the drive one, the other - the idler one. Belt conveyors are widely used in the chemical, metallurgical, machine-building industry, for production of building materials, transport and industrial construction, at the coal preparation plants.
The main publications that describe the structure, design features, operational and design parameters of the conveyors are [4, 5, 6, 7, 8, 9, 10].
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The analysis of publications shows that for determining the conveyor drive parameters, particularly its power, it is necessary to conduct calculation for its pulleys, pulling element (belt), pulling calculation and to select the basic drive elements. The procedure of these calculations is described in detail in [7, 8]. But the use of traditional conveyor drive calculation methods takes some time. Today, the constant development of almost all industries demands more rapid decision-making in the design of continuous-transport machines, which are elements of the production lines. Therefore, to improve the belt conveyor drive design process it is desirable to determine a scheme that allows using the more simple and quick calculations to determine the necessary value of the drive power depending on the design parameters. Such a scheme is proposed for elevators in [2, 3].
Purpose
The work aims to build the parametric dependence for drive power of the belt conveyor with sloping and horizontal areas on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions.
Methodology
The value of belt conveyor drive power depends on many factors. The main parameters affecting its value are: type of load, design efficiency, load lifting height and conveying distance, required load transportation path configuration, conveyor operation conditions. The design diagram
of the conveyor under study and its approximate belt tension chart are shown in Figure 1.
Initial data for design calculations of the examined belt conveyor are as follows:
- Transported material;
- Conveyor efficiency;
- Height or angle of the conveyor sloping area, H or p respectively;
- Lengths of conveyor sections and radius:
Z12 , ¿34 , L56 , Lr56 , L67 , L78 , R1 m.
Fig. 1. Belt conveyer: a - design diagram; b - belt tension chart
For further study we determine that the conveyor has grooved three-roller idlers with 20o angle on the loaded belt and row straight idlers - on the return belt.
Taking into account the data of the tables 8.1 and 8.2 of [8] we present in Table 1 the basic properties of the load that are needed for further calculations:
Table 1
Belt speed and load properties
Bulk load material density p, t/m3 coefficient kcs Belt speed, m/s, at the width, mm
400 500 and 650 800...1 200 1 200. 1 600 1 800. 2 000
sand 1.4 - 1.65 470 1.3 1.5 2.6 3.3 5.5
peat 0.33 - 0.4 550 1.3 1.5 2.6 3.3 5.5
soil 1.1 - 1.6 470 1.3 1.5 2.6 3.3 5.5
gravel 1.5 - 1.9 470 1.1 1.3 1.8 2.6 3.6
stones 1.8 - 2.2 550 - 1.3 1.3 1.8 2.6
coal 0.8 - 1.0 470 1.1 1.3 1.4 1.8 -
cement 1.0 - 1.8 470 - 1.1 1.0 - -
crushed stone 1.3 - 1.8 550 1.1 1.3 1.8 2.6 3.6
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The belt speed values in Table 1 are counted as the mean in a given range of possible values for the set load.
The belt width required for the set efficiency E is calculated by the formula
Be > 1,1
'kcskßPV
0,05
(1)
where kcs - cross-section coefficient of the material on belt (Table 1); kp - coefficient for cross-
section decrease of the material on belt due to its partial bulking into the side opposite to the travel direction (p. 403, [8]); p - bulk density of transported material (Table 1), t/m3.
The determined belt width value is rounded up to the nearest biggest number of a standard row of belt width: 400; 500; 650; 800; 1 000, 1 200 mm.
For convenience of further research, we will do some algebraic transformation in the expression (1). The result is as follows:
kcspv(0,91B -0,05)2 >■
(2)
For unambiguous determination of the required width to achieve the conveyor design efficiency the ratio E/kp must appertain to some range of
values. These ranges are shown in Table 2. The value E/kp depends on the belt width, type of load
and accepted load material density. The limit values of the ranges in Table 2 are calculated for the corresponding limit values of material density. For example, for sand and belt width B = 400 mm the range of variation is E/kp = 84.3 - 99.4, herewith
84.3 corresponds to the sand density 1.4 t/m3 and
99.4 - to the sand density 1.65 t/m3.
Example of usage of Table 1: let the load be soil with the density p = 1.6 t/m3, the
angle p = 22° and the required efficiency E = 64t/h. With the help of (p. 403 [8]) we get: kp = 0.76. We calculate the ratio
E/kp = 64/0.76 = 84.2 < 99.4 , thus, this value corresponds to the width of the belt B = 400 mm. This width is taken for further calculations.
It should also be noted that the inequality sign must be considered in the ratio (2) as follows: the
soil density p = 1.6 t/m3 and belt width B = 400 mm go with the range of values E/kp [0...96.4], B = 500 mm - the range E/kp [96.4.185], B = 650 mm - the range E/kp [185.330.7], B = 800 mm - the range E/kp [330.7.898.8], B = 1000 mm - the range E/kp [898.8.1 446.1], B = 1200 mm - the range E/kp [1446.1.2 694.4]. Accordingly, the soil density p = 1. 1 t/m3 and belt width B = 400 mm go with the range of values E/kp [0.66.3], B = 500 mm - the range E/kp [66.3.127.2], B = 650mm - the range E/kp [127.2.227.4], B = 800mm - the range E/kp [227.4.617.9], B = 1000 mm - the range E/kp [617.9.994.2], B = 1200 mm - the range E/kp
[994.2.1852.4]
For further calculation the conveyor pulling element circuit is divided into straight and curved sections (see Fig. 1a). To determine the belt tension we use the method of pulling calculation by circuit.
We adopt the conveyor drive with one driving pulley, the wrap angle of which is y = 180°. The
pulley surface is lined with rubber.
The efforts in the belt entering the drive pulley are determined by Euler's formula:
Seb = S8 ^ S1e
W
(3)
where ^ - friction factor between the belt and the pulley surface; y - belt wrap angle of drive pulley,
radian; ew - pulling factor (Table 3).
There are two unknown terms Sx and S8 in the equation (3). To formulate the second equation it is necessary to encircle the pulling circuit from point 1 to point 8, expressing the tension at all points through the tension at point 1. The specific weight of the material on belt is determined by the formula
„ Eg
3.6v
= ßE.
(4)
where ß =
g
3.6v
belt speed, N-s/kg-m.
- coefficient that depends on the
ß
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The specific weight of moving parts of upper and lower idlers is determined by formulas:
qUI = g'J il, q = G"J,
(5)
(6)
where Gi, G" - weight of rotating parts of upper and lower idlers respectively.
The spacing of upper and lower idlers li on the path is taken according to the table 8.3 [8]. The lower row idlers are arranged with the double li spacing.
Using the data from tables 8.3 - 8.5 [8] and the formulas (5) - (6) we calculate the specific weight of moving parts of upper and lower idlers. The following table shows the values of the specific weight of moving parts of upper and lower idlers depending on the belt width and load density.
Using the data in table 1 and the formula (4), we built dependence of the loaded material specific weight on the belt width and the conveyor efficiency. The resulted data are shown in Table 5.
Table 2
Ranges of ratio values Ejk^ corresponding to type of load and belt width
Bulk material density p, Ranges of ratio values Elk„ , t/h, with the belt width, mm
load t/m3
400 500 650 800 1 000 1 200
sand 1.4 - 1.65 84,3- 161,9- 289,4-341,1 786,5- 1265,3- 2357,6-
99,4 190,8 926,9 1491,3 2778,6
peat 0.33 - 0.4 23.328.2 44.6-54.1 79.8-96.7 216.9262.9 349-423 650.3-788.3
soil 1.1 - 1.6 66.396.4 127.2-185 227.4-330.7 617.9898.8 994.2-1446.1 1852.42694.4
grave l 1.5 - 1.9 76.596.9 150.3190.4 268.7-340.4 583.3738.9 938.5-1188.8 1990.22520.9
stone s 1.8 - 2.2 - 211.1-258 377.3-461.2 591.6723.1 951.9-1163.4 1934.82364.8
coal 0.8 - 1.0 40.8-51 80.2-100.2 143.3-179.1 242-302.5 389.4-486.7 734.88-918.6
ce- 1.0 - 1.8 - 84.8-152.6 151.6-272.8 216.1- 347.6-625.7 -
ment 388.9
crush ed stone 1.3 - 1.8 77.6107.4 152.5211.1 272.6-377.4 591.6819.2 951.9-1318 2018.52794.8
Table 3
Value of pulling factor e
|iy
Y , grad (radian)
180 (3.14) 190 (3.22) 200 (3.50) 210 (3.67) 240 (4.19)
0.2 (without lining) 1.88 1.94 2.01 2.08 2.31
0.3 (with wood lining) 2.57 2.71 2.85 3.01 3.52
0.4 (with rubber lining) 3.52 3.78 4.05 4.34 5.35
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Table 4
Specific weight of moving parts of upper and lower idlers
Belt width, mm qui at load density p , N/m qu at load density p , N/m
up to 1 t/m3 1...2 t/m3 above 2 t/m3 up to 1 t/m3 1.2 t/m3 above 2 t/m3
400 66.7 71.4 76.9 20 21.5 23.1
500 76.7 82.1 88.5 25 26.8 28.9
650 89.3 96.2 104.2 37.5 40.4 43.8
800 157.1 169.2 183.3 61.1 71.2 77.1
1 000 192.3 208.3 227.3 84.6 91.7 100
1 200 223.1 241.7 263.6 96.2 104.2 113.7
Table 5
Dependence of loaded material specific weight qm on belt width and conveyor efficiency
Bulk load Belt width, mm
400 500 та 650 800.1200 1200.21600 1800.2000
sand 2.14E 1.85E 1.07E 0.84E 0.51E
peat 2.14E 1.85E 1.07E 0.84E 0.51E
soil 2.14E 1.85E 1.07E 0.84E 0.51E
gravel 2.53E 2.14E 1.54E 1.07E 0.77E
stones - 2.14E 2.14E 1.54E 1.07E
coal 2.53E 2.14E 1.98E 1.54E -
cement - 2.53E 2.78E - -
crushed stone 2.53E 2.14E 1.54E 1.07E 0.77E
For clarity in subsequent calculations we adopt as a working element the conveyor fabric-ply belt by GOST 20-85 BKNL-150, whose gasket tensile strength Sp = 150 N/mm. In addition, further on
we will assume that the conveyor operation conditions are heavy or very heavy.
The belt thickness is determined by the formula
8b = 8o + /8 _
(7)
where SG, Sn - thickness of rubber gaskets from
operating and non- operating belt sides; Sg -
thickness of one fabric gasket; S = 1.6 mm for
BKNL-150-type belts.
The gasket thickness is selected subject to heavy operation conditions of the conveyor, so So = 6 mm, Sn = 2 mm, while
5b = 6 + i -1.6 + 2 = 8 + i • 1.6 mm.
The belt running meter weight is calculated by the formula
qb = 0.01B8b ,
(8)
where B and 5b should be substituted in millimetres.
Using the formulas (7) - (8) we obtained the dependence of the belt linear weight value on the number of gaskets and the belt width (Table 6).
The basic principle of the encirclement method is to identify the specific points of the path, where there are changes of belt tension. Herewith the tension in the following (i +1) point equals the sum of the belt tension in this ( i ) point and the belt transport resistance at the section between these points:
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S+1 = S, + Wui+1.
(9)
Belt tension at point 2 is calculated by the formula
= S + Wu, (10)
where W12 - belt transport resistance at the section between the points 1 and 2;
W12 = wLr ( qb + q, ) •
(11)
where w - belt transport resistance (Table 7), which depends on the type of bearing, lubrication, sealing, dustiness of atmosphere and other conditions.
For further research it is assumed that w = 0.03 (operation conditions are heavy, lower idlers are straight, upper idlers are grooved). Using the tables 5 and 6, we obtained the expressions for tension force values at point 2, depending on the belt width and load density (Table 8).
Belt tension at point 3 is calculated by the formula
S3 = kS2, (12)
where k - coefficient for increase in belt tension due to idler pulley rotating resistance (Table 9).
Table 6
Belt linear weight
Belt width B , mm Belt linear weight at i = 3, N/m Belt linear weight at i = 4 , N/m Belt linear weight at i = 5 , N/m Belt linear weight at i = 6 , N/m
400 51.2 57.6 64 70.4
500 64 72 80 88
650 83.2 93.6 104 114.4
800 102.4 115.2 128 140.8
1 000 128 144 160 176
1 200 153.6 172.8 192 211.2
Table 7
Value of coefficient w
Conveyor operation conditions Idlers
straight grooved
Light 0.018 0.020
Average 0.022 0.025
Heavy, very heavy 0.030 Belt tension at point 2 0.030 Table 8
Belt width, mm S2 at load density p , N/m
up to 1 t/m3 1.2 t/m3 above 2 t/m3
400 S1+0.03Ll(qb+20) S1+0.03Ll(qb+21.5) S1+0.03Ll(qb+23.1)
500 S1+0.03Ll(qb+25) S1+0.03Ll(qb+26.8) S1+0.03Ll(qb+28.9)
650 S1+0.03Ll(qb+37.5) S1+0.03Ll(qb+40.4) S1+0.03Ll(qb+43.8)
800 S1+0.03Ll(qb+61.1) S1+0.03Ll(qb+71.2) S1+0.03Ll(qb+77.1)
1 000 S1+0.03Ll(qb+84.6) S1+0.03Ll(qb+91.7) S1+0.03Ll(qb+100)
1 200 S1+0.03Ll(qb+96.2) S1+0.03Ll(qb+104.2) S1+0.03Ll(qb+113.7)
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In the considered conveyor design the belt wrap angle of pulley is less than 90o (Fig. 1), thus k = 1.03.
Table 9
Value of coefficient k
Belt wrap angle of pulley, degrees k
<90 1.03
90 1.04
180 1.05
Dependencies for tension force values at point 5 by belt width and load density are shown in Table 12.
Belt tension at point 6 is calculated by the formula
S6 = S + W56,
(16)
Dependencies to determine the tension force value at point 3 by belt width and load density are shown in Table 10.
Belt tension at point 4 is calculated by the formula
S4 = S3 + W34, (13)
where W34 - belt transport resistance at the section between the points 3 and 4;
W34 = qbL34 (w •cosP - sinP) + qnL34w , (14) where w - belt transport resistance coefficient
(Table 7).
If w = 0.03 (operation conditions are heavy, lower idlers are straight), then the dependences for tension force values at point 4 by belt width and load density are shown in Table 11.
Belt tension at point 5 is calculated by the formula
S5 = k S4, (15)
where k - coefficient for increase in belt tension due to idler pulley rotating resistance (Table 9).
In the considered conveyor design the belt wrap angle of pulley is 180o (Fig. 1), therefore, we assume that k = 1.05 .
where W56 - belt transport resistance at the section between the points 5 and 6;
W56 = (qm + qb )L56 (w • cosP + sinp) + q„iL56w , (17)
where w - belt transport resistance coefficient (Table 7).
If w = 0.03 (operation conditions are heavy, upper idlers are grooved), then the dependences for tension force values at point 6 by belt width and load density are shown in Table 13.
Belt tension at point 7 is calculated by Euler's formula:
о о wa S7 = S6e
(18)
where w - friction factor between the belt and the idler surface; a - belt wrap angle of battery of idlers, radian.
Belt wrap angle of battery of idlers:
a = ■
L67
R
(19)
Dependencies for tension force values at point 7 by belt width and load density are shown in Table 14.
Table 10
Belt tension at point 3
Belt width, mm S3 at load density p , N/m
up to 1 t/m3 1.2 t/m3 above 2 t/m3
400 1.03 S1+0.031Li(qb+20) 1.03 Sj+0.031Ll(qb+21.5) 1.03 S1+0.031Ll(qb+23.1)
500 1.03 S1+0.031Ll(qb+25) 1.03 Sj+0.031Ll(qb+26.8) 1.03 Sj+0.031Ll(qb+28.9)
650 1.03 S1+0.031Ll(qb+37.5) 1.03 S1+0.031Ll(qb+40.4) 1.03 Sj+0.031Ll(qb+43.8)
800 1.03 S1+0.031Ll(qb+61.1) 1.03 Sj+0.031Ll(qb+71.2) 1.03 S1+0.031Ll(qb+77.1)
1 000 1.03 S1+0.031Ll(qb+84.6) 1.03 S1+0.031Ll(qb+91.7) 1.03 S1+0.031Ll(qb+100)
1 200 1.03 S1+0.031Ll(qb+96.2) 1.03 S1+0.031Ll(qb+104.2) 1.03 S1+0.031Ll(qb+113.7)
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Table 11
Belt tension at point 4
Belt width, S4 at load density p , N/m
mm up to 1 t/m3 1.2 t/m3 above 2 t/m3
1.03^+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+
400 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+0.62(Ll+L34) +0.66(Ll+L34) +0.72(Ll+L34)
1.03^+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+
500 +Ls4cosß-32.3Ls4sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+0.77(Ll+L34) +0.83(Ll+L34) +0.9(Ll+L34)
1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+
650 +Ls4cosß-32.3Ls4sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+1.16(Ll+L34) +1.25(Ll+L34) +1.35(Ll+L34)
1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+
800 +Ls4cosß-32.3Ls4sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+2.1(Ll+L34) +2.2(Ll+L34) +2.39(Ll+L34)
1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+
1 000 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+2.6(Ll+L34) +2.84(Ll+L34) +3.1(LI+L34)
1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+ 1.03Sj+0.031 qb(Ll+
1 200 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+2.98(Ll+L34) +3.23(Ll+L34) +3.5(Li+L34)
Table 12
Belt tension at point 5
Belt width, S5 at load density p , N/m
mm up to 1 t/m3 1.2 t/m3 above 2 t/m3
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
400 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+0.65(Ll+L34) +0.7(Ll+L34) +0.75(Ll+L34)
1.08Sj+0.033 qb(Ll+ 1.08Si+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
500 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+0.81(Ll+L34) +0.87(Ll+L34) +0.94(Ll+L34)
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
650 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+1.23(Ll+L34) +1.31(Ll+L34) +1.42(Ll+L34)
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
800 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+2.15(Ll+L34) +2.31(Ll+L34) +2.5(Ll+L34)
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End of table 12
Belt width, S5 at load density p , N/m
mm up to 1 t/m3 1.2 t/m3 above 2 t/m3
1.08Sj+0.033 qb(L++ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
1 000 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+2.75(Ll+L34) +2.98(Ll+L34) +3.25(Ll+L34)
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
1 200 +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+ +L34cosß-32.3L34sinß)+
+3.13(Ll+L34) +3.39(Ll+L34) +3.7(Li+L34)
Table 13
Belt tension at point 6
S6 at load density p , N/m
Belt width, mm
up to 1 t/m3 1.2 t/m3 above 2 t/m3
1.08Si+0.033 qb(Ll+ 1.08Sj+0.033 qb(L+ 1.08Sj+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56-- +(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- -
400 L34)sinß)+ L34)sinß)+ L34)sinß)+
+0.65(Ll+L34+3.08 L56)+ +0.7(Ll+L34+3.06 L56)+ +0.75(Ll+L34+3.08 L56)+
+ qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß)
1.08Si+0.033 qb(Ll+ 1.08Sj+0.033 qb(L\+ 1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56-- +(L34 + L56)cosß+32.3(L56- - +(L34 + Ls6)cosß+32.3(Ls6- -
500 L34)sinß)+ L34)sinß)+ L34)sinß)+
+0.81(Ll+L34+2.82 L56)+ +0.87(Ll+L34+2.84 L56)+ +0.94(Ll+L34+2.82 L56)+
+ qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß)
1.08Si+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56-- +(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- -
650 L34)sinß)+ L34)sinß)+ L34)sinß)+
+1.23(Ll+L34+2.18 L56)+ +1.41(Ll+L34+2.2 L56)+ +1.43(Ll+L34+2.2 L56)+
+ qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß)
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56-- +(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- -
800 L34)sinß)+ L34)sinß)+ L34)sinß)+
+2.15(Ll+L34+2.2 L56)+ +2.31(Ll+L34+2.2 L56)+ +2.5(Ll+L34+2.2 L56)+
+ qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß)
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56-- +(L34 + L56)cosß+32.3(L56- - +(L34 + Ls6)cosß+32.3(Ls6- -
1 000 L34)sinß)+ L34)sinß)+ L34)sinß)+
+2.75(Ll+L34+2.1 L56)+ +2.98(Ll+L34+2.1 L56)+ +3.25(Ll+L34+2.1 L56)+
+ qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß)
1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+ 1.08Sj+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56-- +(L34 + L56)cosß+32.3(L56- - +(L34 + Ls6)cosß+32.3(Ls6- -
1 200 L34)sinß)+ L34)sinß)+ L34)sinß)+
+3.13(Ll+L 34+2.14 L56)+ +3.39(Ll+L34+2.14 L56)+ +3.7(Ll+L34+2.14 L56)+
+ qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß) + qmL56 (0.03cosß+sinß)
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НЕТРАДИЦШШ ВИДИ ТРАНСПОРТУ. МАШИНИ ТА МЕХАШЗМИ
Table 14
Belt tension at point 7
Belt width, mm S7 at load density p , N/m
up to 1 t/m3 1.2 t/m3 above 2 t/m3
ewa [1.08Si+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- -
400 L34)sinß)+ L34)sinß)+ L34)sinß)+
+0.65(Ll+L34+3.08 L56)+ +0.7(Ll+L34+3.06 L56)+ +0.75(Ll+L34+3.08 L56)+
+ qmLs6 (0.03cosß+sinß)] + qmLs6 (0.03cosß+sinß)] + qmLs6 (0.03cosß+sinß)]
ewa [1.08Si+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- - +(L34 + L56)cosß+32.3(L56- -
500 L34)sinß)+ L34)sinß)+ L34)sinß)+
+0.81(Ll+L34+2.82 L56)+ +0.87(Ll+L34+2.84 L56)+ +0.94(Ll+L34+2.82 L56)+
+ qmLs6 (0.03cosß+sinß)] + qmLs6 (0.03cosß+sinß)] + qmLs6 (0.03cosß+sinß)]
ewa [1.08Si+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- - +(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- -
650 L34)sinß)+ L34)sinß)+ L34)sinß)+
+1.23(Ll+L34+2.18 L56)+ +1.41(Ll+L34+2.2 L56)+ +1.43(Ll+L34+2.2 L56)+
+ qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)]
ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+
+(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- -
800 L34)sinß)+ L34)sinß)+ L34)sinß)+
+2.15(Ll+L34+2.2 L56)+ +2.31(Ll+L34+2.2 L56)+ +2.5(Ll+L34+2.2 L56)+
+ qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)]
ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+
+(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- -
1 000 L34)sinß)+ L34)sinß)+ L34)sinß)+
+2.75(Ll+L34+2.1 L56)+ +2.98(Ll+L34+2.1 L56)+ +3.25(Ll+L34+2.1 L56)+
+ qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)]
ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+ ewa [1.08Sj+0.033 qb(Ll+
+(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- - +(L34 + Ls6)cosß+32.3(Ls6- -
1 200 L34)sinß)+ L34)sinß)+ L34)sinß)+
+3.13(Ll+L 34+2.14 L56)+ +3.39(Ll+L34+2.14 L56)+ +3.7(Ll+L34+2.14 L56)+
+ qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)] + qmL56 (0.03cosß+sinß)]
where w - belt transport resistance coefficient (Table 7).
If w = 0.03 (operation conditions are heavy, upper idlers are grooved), then the dependences for tension force values at point 8 by belt width and load density are shown in Table 15.
Belt tension at point 8 is calculated by the formula
S8 = S7 + W78, (20)
where W78 - belt transport resistance at the section between the points 7 and 8;
W78 =( + %b + %ui ) L78w , (21)
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Table 15
Belt tension at point 8
Belt width, mm S8 at load density p , N/m
up to 1 t/m3 1.2 t/m3 above 2 t/m3
^[1.08^+0.033 qb(Ll+ ewa[1.08Sj+0.033 qb(Ll+ ^"[1.08^+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
400 -L34)sinß+Lv8/ewa)+0.65(Ll+ -L34)sinß+L78/ewa)+0.7(Ll + -L34)sinß+L78/ewa)+0.75(Ll +
+L34+3.08 (L56+L78/ ewa))+ +L34+3.06 (L56+L78/ ewa))+ +L34+3.08 (L56+L78/ esa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ О]
ewa[1.08Sj+0.033 qb(Ll+ ewa[1.08Sj+0.033 qb(Ll+ esa[1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
500 -L34)sinß+L78/ewa)+0.81(Ll+ -L34)sinß+L78/ewa)+0.87(Ll + -L34)sinß+L78/ewa)+0.94(Ll +
+L34+2.82 (L56+L78/ ewa))+ +L34+2.84 (L56+L78/ ewa))+ +L34+2.82 (L56+L78/ esa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ esa)]
ewa[1.08Sj+0.033 qb(Ll+ ewa[1.08Sj+0.033 qb(Ll+ ewa[1.08S!+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- -
650 -L34)sinß+L78/ewa)+1.23(Ll+ -L34)sinß+L78/ewa)+1.31(Ll + L34)sinß+L78/ewa)+1.43(Ll+
+L34+2.18 (L56+L78/ ewa))+ +L34+2.2 (L56+L78/ ewa))+ +L34+2.2(L56+ L78/ esa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ esa)]
ewa[1.08Sj+0.033 qb(Ll+ ewa[1.08Sj+0.033 qb(Ll+ esa[1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
800 -L34)sinß+L78/ewa)+2.15(Ll+ -L34)sinß+L78/ewa)+2.31(Ll + -L34)sinß+L78/esa)+2.51(Ll +
+L34+2.2 (L56+L78/ ewa))+ +L34+2.2 (L56+L78/ ewa))+ +L34+2.2 (L56+L78/ esa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ esa)]
ewa[1.08Sj+0.033 qb(Ll+ ewa[1.08Sj+0.033 qb(Ll+ esa[1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
1 000 -L34)sinß+L78/ewa)+2.75(Ll+ -L34)sinß+L78/ewa)+2.98(Ll + -L34)sinß+L78/esa)+3.25(Ll +
+L34+2.1 (L56+L78/ ewa))+ +L34+2.1 (L56+L78/ ewa))+ +L34+2.1 (L56+L78/ esa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ esa)]
ewa[1.08Sj+0.033 qb(Ll+ ewa[1.08Sj+0.033 qb(Ll+ esa[1.08Si+0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
1 200 -L34)sinß+L78/ewa)+3.13 (L+ -L34)sinß+L78/ewa)+3.39(Ll + -L34)sinß+L78/esa)+3.7(Ll +
+L34+2.14 (L56+L78/ ewa))+ +L34+2.14 (L56+L78/ ewa))+ +L34+2.14 (L56+L78/ esa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ esa)]
Findings
For convenience of further research we depict the dependencies of the table 15 in the following Solving the system of equations for the limiting form: state, in which there is no pulley slipping, we get:
doi 10.15802/stp2016/61024 © V. M. Bohomaz, 2016
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S„ = ew< S,
1 5
P = F0v/1 000n
(26)
S8 = 1.08ewa Sj +
+fb ,p( qb, Li ß, Im ( E ) ).
(22)
Now equating the right parts of expressions (22), we get:
em S1 = L08ewa S1 +
+fbA qb, Li , L34, L56 , L78 , P, 1 m (E)) .
Using algebraic manipulations we obtain:
S = FB,p (qb , Ll,L34 , L56 ,L78 ,P, qm (E)) (23) Si =-;-;-, (23)
where Fo should be substituted in Newton; v - in
meters per second; n - drive efficiency factor.
The drive efficiency factor is determined by the formula:
П = ППс,
(27)
where n = 0.96 - reduction gear efficiency factor; nc = 0.98 - coupling efficiency factor. Thus
n = nr nc =0.96 -0.98 = 0.94.
S = em
(Y - 1.08ewa)
FB,p ( qb , Ll, L34, L56, L78,ß, qm (E) )
(Y - 1.08ewa)
. (24)
The pulling effort considering the drive pulley rotation resistance is determined by the formula
F0 = S8 -S, + (k'-1)(S8 +
(25)
Fig. 2. Belt conveyer drive diagram:
1 - motor; 2 - elastic coupling; 3 - brakes; 4 - reduction gear; 5 - gear coupling; 6 - drive pulley; 7 - belt
The installed motor power (kW) is calculated where k ' = 1.08 - drive pulley rotation resistance by the formula
coefficient.
Substituting the expressions (23) and (24) into the formula (25) we get:
Fa = (l.08e^Y - 0.92)x
FB,p (%b , Ll, L34 , L56 , L78 , P, %m (E) ) X (Y-1.086"°) .
The belt conveyor drive is more often designed
Pq = nfr,
(28)
where ni = 1. 1... 1.2 - power reserve factor.
Choosing n = 1.2 we determine the installed motor power by the formula:
F v
P =-
(29)
833.3n
Dependencies for the motor power value by
with cylindrical double reduction gear. The kine- belt width and load density are shown in Table 16. matic diagram of the drive is shown in Fig. 2.
Rated motor power is calculated by the formula
Calculated drive power
Table 16
Belt width, mm P at load density p , N/m
up to 1 t/m3 1.2 t/m3 above 2 t/m3
400 [v(1.08ew- 0.92)ewa/833.3n(e"Y- -1.08 ewa)] [0.033 qb(Ll+ +(L34 + L56)cosß+32.3(L56--L34)sinß+L78/ewa)+0.65(Ll+ +L34+3.08 (L56+L78/ ewa))+ + qm (L56 (0.03cosß+sinß) +0.03L78/ ewa)] [v(L08ew-0.92)eM"7833.3n(ew --1.08 ewa)] [0.033 qb(Ll+ +(L34 + L56)cosß+32.3(L56--L34)sinß+L78/ewa)+0.7(Ll + +L34+3.06 (L56+L78/ ewa))+ + qm (L56 (0.03cosß+sinß) +0.03L78/ ewa)] [v(1.08e^Y-0.92)ewa/833.3n(e^Y --1.08 ewa)] [0.033 qb(Ll+ +(L34 + L56)cosß+32.3(L56--L34)sinß+L78/ewa)+0.75(Ll + +L34+3.08 (L56+L78/ ewa))+ + qm (L56 (0.03cosß+sinß) +0.03L78/ ewa)]
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End of table 16
P at load density p , N/m
Belt width, mm
up to 1 t/m3 1.2 t/m3 above 2 t/m3
^(1.08^-0.92^7833.3^ [v(L08ew-0.92)eM"7833.3n(ew [v(L08ew-0.92)eM"7833.3n(ew
"-1.08 ewa)] [0.033 qb(L+ --1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
500 -L34)srnß+L78/0+0.81(Ll+ -L34)sinß+L78/ewa)+0.87(Ll + -L34)sinß+L78/ewa)+0.94(Ll +
+L34+2.82 (L56+L78/ ewa))+ +L34+2.84 (L56+L78/ ewa))+ +L34+2.82 (L56+L78/ ewa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ ewa)]
[v(1.08e"Y-0.92)ewa/833.3n(e"Y [v(L08ew-0.92)eM"7833.3n(ew [v(L08ew-0.92)eM"7833.3n(ew
--1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- -
650 -L34)sinß+L78/ewa)+1.23(Ll+ -L34)sinß+L78/ewa)+1.31(Ll + L34)sinß+L78/ewa)+1.43(Ll+
+L34+2.18 (L56+L78/ ewa))+ +L34+2.2 (L56+L78/ ewa))+ +L34+2.2(L56+ L78/ ewa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ ewa)]
[v(1.08e"Y-0.92)ewa/833.3n(e"Y [v(L08ew-0.92)eM"7833.3n(ew [v(L08ew-0.92)eM"7833.3n(ew
--1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
800 -L34)sinß+L78/ewa)+2.15(Ll+ -L34)sinß+L78/ewa)+2.31(Ll + -L34)sinß+L78/ewa)+2.51(Ll +
+L34+2.2 (L56+L78/ ewa))+ +L34+2.2 (L56+L78/ ewa))+ +L34+2.2 (L56+L78/ ewa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ ewa)]
[v(1.08e"Y-0.92)ewa/833.3n(e"Y [v(L08ew-0.92)eM"7833.3n(ew [v(L08ew-0.92)eM"7833.3n(ew
--1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
1 000 -L34)sinß+L78/ewa)+2.75(Ll+ -L34)sinß+L78/ewa)+2.98(Ll + -L34)sinß+L78/ewa)+3.25(Ll +
+L34+2.1 (L56+L78/ ewa))+ +L34+2.1 (L56+L78/ ewa))+ +L34+2.1 (L56+L78/ ewa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ ewa)]
1 2 3 4
[v(1.08e"Y-0.92)ewa/833.3n(e"Y [v(L08ew-0.92)eM"7833.3n(ew [v(L08ew-0.92)eM"7833.3n(ew
--1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+ --1.08 ewa)] [0.033 qb(Ll+
+(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56- +(L34 + L56)cosß+32.3(L56-
1 200 -L34)sinß+L78/ewa)+3.13(Ll+ -L34)sinß+L78/ewa)+3.39(Ll + -L34)sinß+L78/ewa)+3.7(Ll +
+L34+2.14 (L56+L78/ ewa))+ +L34+2.14 (L56+L78/ ewa))+ +L34+2.14 (L56+L78/ ewa))+
+ qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß) + qm (L56 (0.03cosß+sinß)
+0.03L78/ ewa)] +0.03L78/ ewa)] +0.03L78/ ewa)]
Originality and practical value
We developed parametric dependence of drive power of the belt conveyer with sloping and horizontal areas on type of load, design efficiency, geometrical dimensions and path configuration, operation conditions that takes into account standard
dimensions and parameters of belts, idlers and pulleys.
Use of the built dependences gives an opportunity of relatively rapid determination of approximate value of the drive power for the belt conveyers of considered design, as well as it allows qual-
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету затзничного транспорту, 2016, № 1 (61)
ity selection of its basic elements at specific design characteristics and requirements.
The proposed dependences can be used for determination of general impact of the design efficiency and other parameters on the conveyor drive power.
Conclusions
For belt conveyors with sloping and horizontal areas we built parametric dependence of drive power on the design parameters: type of load, design efficiency, geometrical dimensions and path configuration, operation conditions. Such dependences allow calculating the required drive power value, taking into account the type and the physical and mechanical properties of load, the lifting height value, the transport length and design efficiency, using only one formula, chosen depending on design characteristics.
LIST OF REFERENCE LINKS
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3. Богомаз, В. М. Дослвдження впливу проектно! продуктивносп елеватору на потужшсть його приводу / В. М. Богомаз, К. Ц. Главацький, О. А. Мазур // Наука та прогрес транспорту. -2015. - № 2 (56). - С. 189-206. doi: 10.15802/stp2015/42178.
4. Зенков, Р. Л. Машины непрерывного транспорта : учебник / Р. Л. Зенков, И. И. Ивашков, Л. Н. Колобов. - Москва : Машиностроение, 1987. - 432 с.
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9. Расчет и проектирование транспортних средств непрерывного действия : научное пособие для вузов / А. И. Барышев, В. А. Будишевский, А. А. Сулима, А. М. Ткачук. - Донецк : Норд-Пресс, 2005. - 689 с.
10. Ромакин, Н. Е. Машины непрерывного транспорта : учебн. пособие / Н. Е. Ромакин. - Москва : Академия, 2008. - 432 с.
11. Jamaludin, J. Development of a self-tuning fuzzy logic controller for intelligent control of elevator systems / J. Jamaludin, N. A. Rahim, W. P. Hew // Engineering Applications of Artificia Intelligence. - 2009. - Vol. 22. - Iss. 8. - Р. 1167-1178. doi: 10.1016/j.engappai.2009.04.006.
12. Kim, C. S. Nonlinear robust control of a hydraulic elevator: experiment-based modeling and two-stage Lyapunov redesign / C. S. Kim, K. S. Hong, M. K. Kim // Control Engineering Practice. -2005. - Vol. 13. - Iss. 6. - P. 789-803. doi: 10.1016/j.conengprac.2004.09.003.
13. Strakosch, G. R. The Vertical Transportation Handbook / G. R. Strakosch, R. S. Caporale. -New York : John Wiley&Sons, 2010. - 610 p. doi: 10.1002/9780470949818.
В. М. БОГОМАЗ1*
1 Каф. «Вшськова тдготовка спещалютш Державно! спещально! служби транспорту», Дтпропетровський нацюнальний утверситет залiзничного транспорту iMeHi академжа В. Лазаряна, вул. Лазаряна, 2, Дтпропетровськ, Украша, 49010, тел. +38 (056) 793 19 09, ел. пошта [email protected], ORCID 0000-0001-5913-2671
ДОСЛ1ДЖЕННЯ ЗАЛЕЖНОСТ1 ПОТУЖНОСТ1 ПРИВОДУ СТР1ЧКОВОГО КОНВЕеРУ В1Д ЙОГО ПРОЕКТНИХ ПАРАМЕТР1В
Мета. Привад е одним 1з основних елеменпв стрiчкових конвеeрiв. Для визначення потужносп приводу необхвдно провести розрахунки за стандартними методиками, яш викладеш в сучаснш техшчнш лггератур^ Для таких розрахуншв потрiбно витратити достатньо багато часу. Основними проектними параметрами
<1о1 10.15802^2016/61024 © V. М. БоЬота2, 2016
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 1 (61)
НЕТРАДИЦШШ ВИДИ ТРАНСПОРТУ. МАШИНИ ТА МЕХАШЗМИ
стрiчкового транспортера е: тип вантажу, проектна продуктивнiсть, геометричнi розмiри та конфиуращя траси, умови роботи. В статп необхвдно побудувати параметричну залежнють потужностi приводу ст^чко-вого конвееру вщ проектних параметрiв, яка враховувала б стандартнi розмiри i параметри стрiчок, ролико-опор та барабашв. Методика. Розглядаеться стрiчковий конвеер iз двома дiлянками: похилою та горизонтальною. Використовуючи методику тягового розрахунку способом обходу по контуру ст^чкових конвеерiв, побудовано параметричнi залежностi сил натягу в характерних точках траси конвееру вщ типу вантажу, проектно! продуктивностi, геометричних розмiрiв та конф^рацп траси конвееру, умов роботи. Результата. Для с^чкових конвеерiв розглянутого типу з врахуванням стандартних розмiрiв стрiчки та вiдповiдними припущеннями щодо типу роликоопор та барабанiв побудовано параметричш залежностi потужностi приводу ввд типу вантажу, проектно! продуктивностi, геометричних розмiрiв i конф^рацп траси конвееру, умов роботи. Наукова новизна. Вперше побудована параметрична залежнiсть потужностi приводу ст^чкових конвеерiв iз двома донками (похилою та горизонтальною) вiд типу вантажу, проектно! продуктивносп, геометричних розмiрiв та конфiгурацi! траси конвееру, умов роботи. Вона враховуе стандартш розмiри та параметри стрiчок, роликоопор i барабанiв. Практична значимiсть. Використання побудованих залежнос-тей потужностi приводу стрiчкових конвеерiв iз похилою та горизонтальною дшянками ввд проектних пара-метрiв дае можливiсть вiдносно швидкого визначення приблизного значення потужностi приводу на стади проектування. Також можливим е виконання якiсного пiдбору його основних елеменпв при конкретних проектних характеристиках та вимогах. Запропоноваш залежностi можуть бути використанi для визначення загального характеру залежностi потужностi приводу ввд проектно! продуктивностi.
Ключовi слова: конвеер; стачка; привод; потужнiсть; продуктивнiсть; вантаж
В. Н. БОГОМАЗ1*
1 Каф. «Военная подготовка специалистов Государственной специальной службы транспорта», Днепропетровский национальний университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (056) 793 19 09, эл. почта ^^отаБ^.иа, ОЯСГО 0000-0001-5913-2671
ИССЛЕДОВАНИЕ ЗАВИСИМОСТИ МОЩНОСТИ ПРИВОДА ЛЕНТОЧНОГО КОНВЕЙЕРА ОТ ЕГО ПРОЕКТНЫХ ПАРАМЕТРОВ
Цель. Привод является одним из основных элементов ленточных конвейеров. Для определения мощности привода необходимо провести расчеты по стандартным методикам, которые изложены в современной технической литературе. Для таких расчетов нужно потратить достаточно много времени. Основными проектными параметрами ленточных транспортеров являются: тип груза, проектная производительность, геометрические размеры и конфигурация трассы, условия работы. В статье необходимо построить параметрическую зависимость мощности привода ленточного конвейера от его проектных параметров, которая учитывала б стандартные размеры и параметры лент, роликоопор и барабанов. Методика. Рассматривается ленточный конвейер с двумя участками: наклонным и горизонтальным. Используя методику тягового расчета способом обхода по контуру ленточных конвейеров, построены параметрические зависимости сил натяжения в характерных точках трассы конвейера от типа груза, проектной производительности, геометрических размеров и конфигурации трассы, условий работы. Результаты. Для ленточных конвейеров рассмотренного типа с учетом стандартных размеров ленты и соответствующими предположениями относительно типов роликоопор и барабанов построены параметрические зависимости мощности привода от типа груза, проектной производительности, геометрических размеров и конфигурации трассы, условий работы. Научная новизна. Впервые построена параметрическая зависимость мощности привода ленточных конвейеров с двумя участками (наклонной и горизонтальной) от типа груза, проектной производительности, геометрических размеров и конфигурации трассы, условий работы. Она учитывает стандартные размеры и параметры ленты, роликоопор и барабанов. Практическая значимость. Использование построенных зависимостей мощности привода ленточных конвейеров с наклонным и горизонтальным участками дает возможность относительно быстрого определения приблизительного значения мощности привода на стадии проектирования. Также возможным является выполнение качественного подбора его основных элементов при конкретных проектных характеристиках и требованиях. Предложенные зависимости могут быть использованы для определения общего характера зависимости мощности привода от проектной производительности.
Ключевые слова: конвейер; лента; привод; мощность; производительность; груз
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 1 (61)
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Prof. S. V. Raksha, Sc. Tech. (Ukraine); Assos. Prof. S. V. Shatov, Sc. Tech. (Ukraine) recommended
this article to be published
Accessed: Nov., 20. 2015
Received: Jan., 15. 2016
